1. Field of the Invention
The present invention relates to a musical sound synthesizing apparatus, and in particular, to a musical sound synthesizing apparatus which preferably generates a musical sound having inharmonicity, such as a piano sound, a guitar sound or the like.
2. Description of the Related Art
In general, a wave form of musical sound is composed by synthesizing a plurality of types of sine waves. These sine waves are called overtones (harmonic tones) because their frequency has an integer times relation with a single frequency. In particular, an overtone of the lowest frequency is called a fundamental wave, and the frequency of the fundamental wave is called a fundamental frequency. The frequency of each of the other overtones is an integer times as much as the fundamental frequency. A relative level relation between the overtones is called an overtone structure, and a timbre of musical sound determination depends upon a difference in the overtone structure.
In electronic musical instruments, there is a known overtone synthesis method which is called a sine wave harmonics synthesis method of generating a plurality of sine waves at overtone frequencies, and accumulating these sine waves so as to synthesize a musical sound. According to that method, a fundamental frequency corresponding to a pitch is stored in a memory as a frequency table, and the fundamental frequency is read from the frequency table using the pitch as a key. And then, by multiplying the fundamental frequency by an integer, a frequency of each overtone other than the fundamental frequency is computed (calculated), and these frequencies are synthesized so that a desired musical sound is obtained. Since the fundamental frequency corresponding to a pitch is common in many musical sounds, a memory capacity for storing the aforesaid frequency table can be small. According to the sine wave harmonics synthesis method, a sound having the same overtone structure as a natural musical sound is generated, and thereby, it is possible to reproduce a musical sound close to that of a natural musical instrument.
For example, in musical sounds of natural musical instruments such as a piano, a guitar or the like, a frequency of each overtone is not an exact integer times as much as the fundamental frequency, but is slightly shifted from the integer times. More specifically, in these musical sounds, the frequency of an overtone is slightly higher than the integer times of the fundamental frequency. The higher the degree of overtone is, the larger the shift is. The quality of musical sound as described above is called inharmonicity. The degree of inharmonicity differs depending upon the type of musical instrument, and also, even in the same type of musical instrument, a difference occurs in between lower and higher tones. The inventor of the present invention has already invented a musical sound synthesizing apparatus which can vary an inharmonicity of musical sound according to a pitch of the musical sound, a timbre and touch strength (see Japanese Patent Application No. Hei 9-70908).
Even in the sine wave harmonics synthesis method, the aforesaid musical sound synthesizing apparatus can generate a wave form of an overtone structure closer to the sound of natural instruments having an inharmonicity using a memory with a small capacity for the frequency table. However, the overtone structure of natural instruments is further complicated. FIG. 11 shows a spectrum distribution of a piano sound, and in the figure, the ordinate takes an amplitude (dB) and the abscissa takes a frequency (kHz). In FIG. 11, it is found that in addition to each overtone A having inharmonicity, there exists a frequency component "a" of a relatively high amplitude level different from a noise, adjacent to the overtone A (see a partially enlarged view of FIG. 11). This is called a "spectral split", and a series of split components "a" shows an inharmonicity and an amplitude level which are different from the essential series of overtones A. The essential series of overtones A is called an "upper series"; on the other hand, the series of split components "a" is called a "lower series".
To give an example, the following is an explanation about inharmonicity of a musical sound of a piano. The inharmonicity is expressed by shift .delta.n (cent value) of an n-th overtone frequency fn from an integer times n.f0 of a fundamental frequency f0 (fundamental frequency of an ideal string without elasticity), and is obtained from the following equation (1). EQU .delta.n=1200 log 2 (fn/n.f0) (1)
FIG. 12 shows inharmonicity of a piano sound obtained from the above equation (1). In FIG. 12, the inharmonicity is expressed by a cent value (ordinate). As seen from FIG. 12, the upper series and the lower series are different in inharmonicity, and therefore, it is found that the piano sound comprises the two series of inharmonious overtones which are overlapped and different from each other. Also, a mixture ratio of the upper and the lower series is variable depending upon touch, that is, a note on (key on) strength of a keyboard. In most musical instruments having inharmonicity, the spectral split as described above appears therein. The aforesaid inharmonicity of piano sound and spectral split have been disclosed and discussed in pages 9 to 15 of "TECHNICAL REPORT OF IEICE EA93-28 (1993-07)" published by THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS.